Emulating the mapping between quantities of interest and their control parameters using surrogate models finds widespread application in engineering design, including in numerical optimization and uncertainty quantification. Gaussian process models can serve as a probabilistic surrogate model of unknown functions, thereby making them highly suitable for engineering design and decision-making in the presence of uncertainty. In this work, we are interested in emulating quantities of interest observed from models of a system at multiple fidelities, which trade accuracy for computational efficiency. Using multifidelity Gaussian process models, to efficiently fuse models at multiple fidelities, we propose a novel method to actively learn the surrogate model via leave-one-out cross-validation (LOO-CV). Our proposed multifidelity cross-validation (\texttt{MFCV}) approach develops an adaptive approach to reduce the LOO-CV error at the target (highest) fidelity, by learning the correlations between the LOO-CV at all fidelities. \texttt{MFCV} develops a two-step lookahead policy to select optimal input-fidelity pairs, both in sequence and in batches, both for continuous and discrete fidelity spaces. We demonstrate the utility of our method on several synthetic test problems as well as on the thermal stress analysis of a gas turbine blade.

翻译：利用代理模型模拟感兴趣量与其控制参数之间的映射关系，在工程设计中得到广泛应用，包括数值优化和不确定性量化。高斯过程模型可作为未知函数的概率代理模型，因此非常适用于存在不确定性的工程设计与决策。本研究关注模拟从系统多保真度模型中观测到的感兴趣量，这些模型在计算效率与精度之间进行权衡。通过采用多保真度高斯过程模型来高效融合多保真度模型，我们提出一种基于留一交叉验证（LOO-CV）主动学习代理模型的新方法。我们提出的多保真度交叉验证（\texttt{MFCV}）方法通过建立所有保真度层级LOO-CV误差之间的相关性，开发了一种自适应策略来降低目标（最高）保真度的LOO-CV误差。\texttt{MFCV}构建了前瞻两步策略，可在连续和离散保真度空间中，以序列或批处理方式选择最优的输入-保真度组合。我们在多个合成测试问题以及燃气涡轮叶片热应力分析案例中验证了该方法的有效性。